Download Sample Problems MTH 63

Applied Algebra I
Doug Gardner
Rogue Community College
Rogue Community College
3345 Redwood Highway
Grants Pass, OR 97527-9298
www.roguecc.edu
(541) 956-7500
An Innovative Math in CTE Curriculum:
Funded by an ATE grant from the National Science Foundation:
Principal Investigators:
Doug Gardner
Serena Ota St. Clair
Rogue Community College Mathematics
Chapter Objectives
Chapter 1: Tools of Algebra (page 5)
Section 1.1: Operations with Real Numbers
• +,-,x,÷ Fractions and Decimals
• +,-,x,÷ Negative Numbers
Section 1.2: Measurement
• Measure with cm, mm, and inches
• Convert fractions to decimals
• Convert decimals to fractions
• Round decimal measures to fractions
• Convert feet-inch-fraction
measurements to inches and decimals
Section 1.3: Ratio, Proportion & Percent
• Set up and solve proportion problems
• Convert fractions and decimals to
percents
• Convert percents to fractions and
decimals
• Solve percentage problems
Section 1.4: Dimensional Analysis
• Convert to different units of measure:
length, area, volume, & weight
• Convert from metric to standard units
• Convert from standard to metric units
Section 1.5: Order of Operations
• Understand meaning of an exponent
• Apply order of operations with formulas
Chapter 2: Formulas/Equations (page 63)
Section 2.1: Solving simple equations
• Solving equations with addition,
subtraction, multiplication, and division
Section 2.2: Solving for different Variables
• Solving formulas for different letters
Section 2.3: Solving complex equations
• Solving equations with exponents
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Chapter 3: Right Triangle Geometry (page 85)
Section 3.1: Pythagorean Theorem
• Find the hypotenuse in a right triangle
• Find a leg in a right triangle
• Solve practical problems
Section 3.2: Angles
• Estimate and measure angles in degrees
• Angles with degrees, minutes & seconds
• Solve practical problems
Section 3.3: Trigonometry
• Use sine, cosine & tangent to find missing
sides and angles in right triangles
• Solve practical problems
Chapter 4: Quantitative Geometry (page 113)
Section 4.1: Area & Perimeter
• Find the perimeter of polygons and circles
• Find the area of polygons and circles
• Solve practical problems
Section 4.2: Surface area
• Find the surface area of solids
• Convert to different units of measure
• Solve practical problems
Section 4.3: Volume
• Find the volume of solids
• Convert to different units of measure
• Solve practical problems
Appendix:
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Abbreviations and Symbols
Conversions
Area and Perimeter Formulas
Volume and Surface Area Formulas
Decimal/Fraction Conversions
Steel Design Table
Sample Problems: Math 63
Chapter 1: Tools of Algebra
1. The face frame of a cabinet is made of vertical stiles and horizontal rails. Calculate the width of
the rails in the design below so that all nine rails are the same length.
2. In a gable, each trapezoidal piece of lap siding is
shorter than the one below by the same amount. A
proportion can be used to calculate that amount,
allowing a carpenter to cut the pieces without
taking measurements. The bottom of each piece of
siding is placed 7 inches above the bottom of the
piece below. Use the roof’s slope of 5/12 and the
long point to long point measurement of the first
piece, to set up a proportion and calculate the long
point to long point measurement of the 2nd piece.
Round your answer
to the nearest 16th
of an inch.
Rogue Community College Mathematics
5PL4
3. The uniform load deflection (D) of a beam is D = 384EI .
Note: Deflection is simply a measurement of the
amount of bend in a beam.
D = deflection measured in inches, P = weight on
the beam measured in pounds, L = length of the
beam measured in inches, E = elasticity of the beam
measured in pounds per square inch (PSI), and I =
moment of inertia of the beam measured in
inches4.
Find the deflection of a beam rounded to one decimal place if L = 168 inches,
P = 358 pounds, E = 2,000,000 psi, and I = 968 inches4.
Chapter 2: Formulas/Equations
4. The moment of inertia (I) of a beam is
I=
bd3
12
.
Note: Moment of inertia is a measure of a beam’s
effectiveness at resisting bending based on its crosssectional shape.
I = moment of inertia of the beam measured in inches4,
b = width of the beam measured in inches and d = height
of the beam measured in inches.
Find the height of a beam rounded to the nearest 8th of
an inch if b = 7
1"
and
4
I = 6.5.
5. The point load deflection (D) of a beam is D =
PL3
48EI
.
Note: Deflection is simply a measurement of the amount of bend in a beam.
D = deflection measured in inches, P = weight on the beam measured in pounds,
L = length of the beam measured in inches, E = elasticity of the beam measured in
pounds per square inch (PSI), and I = moment of inertia of the beam measured in
inches4.
Find the length of a beam rounded to the nearest inch if D = .9, P = 3800, E = 1,700,000,
and I = 326.
Rogue Community College Mathematics
Chapter 3: Right Triangle Geometry
6. Studs in a framed wall are placed 16” inches apart. A sloped
wall presents a challenge in that the distance (L) between
studs along the top plate is longer. If the top plate has a
slope of 4/12, calculate distance L so that the stud layout
can be marked on the top plate. Round your answer to the
nearest 16th of an inch. Hint: First use the slope to calculate
the rise for a 16” run.
7. A CNC operator wants to locate five holes in a plate beginning at
the top and evenly spaced around the center. Dividing 360o by
five, he realizes the angle between the holes must be 72o. If the
holes are to be 27 centimeters from the center, use trigonometry
to calculate the distance from the center over (X) and up (Y) to
the center of the hole indicated in the drawing. Round your
answers to one decimal place.
8. Find the total length of angle iron used to construct the roof
truss. Answer to the nearest inch.
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Chapter 4: Quantitative Geometry
9. HVAC (heating, ventilation, air conditioning) contractors
use a boot to transition from the rectangular register
(commonly seen on the floor or ceiling of a house) to a
circular duct. To equalize the pressure, the rectangular end
of the boot should, ideally, have the same area as the
circular end. Calculate the diameter for a circular end that
will match a 6” x 14” rectangular end, rounded to the
nearest whole number.
10. The pipe in the drawing is supported below a beam by
hanging it with strapping. Find the length of strapping
1
needed, rounded to the nearest 8 inch.
11. Find the total volume of the
hip roof in cubic feet, rounded
to one decimal place. Hint:
Think of the roof as two halves
of a pyramid separated by a
triangular prism.
Rogue Community College Mathematics
RCC Mathematics Course Sequence
Rogue Community College Mathematics